Bermuda Rum Swizzle

This is a popular drink in a variety of bars and restaurant in Bermuda. Many travelers coming back from there will ask me for the recipe, only to discover that falernum is rather hard to find up here. Fortunately that is beginning to change, and a few different brands are now available.
To make this as a “true” swizzle, you would use a traditional swizzle stick to mix and froth the drink up.